Theorem ax6b 1541

Description: Quantified Negation. Axiom C5-2 of [Monk2] p. 113.

(Contributed by GD, 27-Jan-2018.)

Assertion

Ref	Expression
ax6b	|- ( -. A. x ph -> A. x -. A. x ph )

Proof of Theorem ax6b

Step	Hyp	Ref	Expression
1		ax-ial 1427	. 2 |- ( A. x ph -> A. x A. x ph )
2	1	ax6blem 1540	1 |- ( -. A. x ph -> A. x -. A. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  hbn1  1542  hbnt  1543